Fourier-Mukai Transforms and Stable Sheaves on Weierstrass Elliptic Surfaces

On a Weierstraß elliptic surface X, we define a “limit” of Bridgeland stability conditions, denoted as-stability, by moving the polarisation towards the fiber direction in the ample cone while keeping the volume of the polarisation fixed. We describe conditions under which a slope stable torsion-free sheaf is taken by a Fourier-Mukai transform to a -stable object, and describe a modification upon which a-semistable object is taken by the inverse Fourier-Mukai transform to a slope semistable torsion-free sheaf. We also study wall-crossing for Bridgeland stability, and show that 1-dimensional twisted Gieseker semistable sheaves are taken by a Fourier-Mukai transform to Bridgeland semistable objects.

• Fecha de publicación: 2024
• Institución: Universidad del Rosario
• Repositorio: Repositorio EdocUR - U. Rosario
• Idioma: eng
• OAI Identifier: oai:repository.urosario.edu.co:10336/44806
• Acceso en línea: https://doi.org/10.1007/s00574-024-00422-7; https://repository.urosario.edu.co/handle/10336/44806
• Palabra clave: Weierstrass surface; Elliptic surface; Fourier-Mukai transform; Stability
• License: Attribution-NonCommercial-NoDerivatives 4.0 International